Nonlinear Finite Element Methods

Nonlinear Finite Element Methods.
University of Colorado at Boulder - Course number ASEN 6107.
This course covers the modeling, formulation and numerical solution of nonlinear problems in structural mechanics by finite element methods. Emphasizes treatment of geometric nonlinearities, applications to assessment of static and dynamic stability, incremental and iterative methods for solution of nonlinear systems of equations and basic computer implementation issues. Both the Total Lagrange and Corotational kinematic descriptions of nonlinear finite elements are treated. The course does not consider material nonlinearities.
since these are covered in advanced Civil Engineering courses..
Syllabus Outline.
Part 1: Overview of Nonlinear Problems.
Sources of nonlinearities in structural problems: material, geometry, forces, boundary conditions. General features of nonlinear.
response: equilibrium trajectories, path dependencies, critical points.
Part.
2. Formulation of Geometrically Nonlinear Finite Elements.
Residual and incremental forms. Finite element Total Lagrangian and corotational formulations. FEM nonlinear equilibrium equations:
initial stress, tangent and secant stiffness, geometric stiffness.
Part.
3. Solution of Nonlinear Equations.
Classification of solution methods. Increment control techniques. Augmented equation methods. Incremental and pseudo-force.
methods. Newton methods. Secant (quasi-Newton) methods. Acceleration and line search. Dynamic relaxation. Determination and.
traversal of critical points.
Part.
4. Computer Implementation of Nonlinear Analysis (concurrent with Parts 2-3).
Model definition. Element level calculations. Equation assembly. Nonlinear equation solver. Residual evaluation. Post-processing.
Part.
5. Applications to Structural Stability.
Linearized prebuckling. Nonlinear stability analysis. Imperfection sensitivity.
Part.
6. Nonconservative Problems.
Follower loads. Load stiffness. Overview of dynamic instability phenomena: divergence, flutter.